While the talks still could collapse, the aim is to have a deal done in two to three weeks, according to the Wall Street Journal, which first reported the transaction.

A takeover of Gambro would be the biggest deal ever for Deerfield-based Baxter, according to the New York Times.

The medical products maker has struck eight deals in the past two years, the Times said, citing data from Standard & Poor’s Capital IQ. But its largest deal to date was a roughly $700 million purchase in 1997.

Both companies have plastics processing operations. The acquisition would help Baxter round out its kidney-dialysis business. Baxter makes machines that perform peritoneal dialysis, which can be done at home. Gambro makes equipment for hemodialysis, which generally is done in a hospital or clinic.

Baxter has been a top performer in the medical products sector, but CEO Robert Parkinson needs to find a way to boost revenue in order to drive the stock price higher, according to a report by analyst Rick Wise of investment firm Stifel Nicolaus & Co., issued before news surfaced of the Gambro negotiations.

“At current share price levels ... we believe in order for the stock to move above the $70 level, we would require greater revenue upside beyond our currently modeled assumptions,” Mr. Wise wrote in the Nov. 19 report.

One person familiar with the companies says Baxter has considered doing a deal with Gambro for years.

Baxter has a market value of about $36 billion and had more than $3 billion in cash as of September. It had sales last year of $13.9 billion and has nearly 50,000 employees.

Gambro, founded in 1964 and owned by two Nordic private-equity firms since 2006, has about 7,500 employees and roughly $1.6 billion in annual sales.

Baxter was founded in 1931 and began trading on the New York Stock Exchange in 1961.